Standard Deviation of Returns

Mutual Fund Bullet Tour Page 14

A group of investing returns over some period of time is a
set of data points.

Standard deviation can best be described as the average
difference between the values of the data points in a set and the mean
of the data points in a set.

The difference between the value of a data point and the
mean is known as its deviation from the mean.

Standard deviation is a measure of volatility. The greater
the standard deviation the higher the volatility and the riskier the
investment.

Published standard deviations are usually annualized
monthly standard deviations rather than the standard deviation of
annual returns.

Standard deviation is the standard measure of investment
risk.

Standard deviation measures the total risk of individual
assets and portfolios of assets in terms of the volatility of returns.

Security returns are known to be approximately normally distributed,
which makes it easy to make some inferences from the value of the
standard deviation. This is because the normal distribution is the
familiar symmetric bell shaped curve and the mean splits the
distribution right down the middle.

The following rules of thumb apply to the normal
distribution.

Span

Probabilty

+/-
1 SD

68%

+/-
2 SD

96%

+/-
3 SD

100%

+/-2 standard deviations is actually 95.44% but, as this
is only a rule of thumb, we'll use 96%, which is easier to divide by
two.

Here's what you should note in the above:

Data points are much more likely to be near the mean than
at the extremes.

There's a 68% probability of a data point falling within
one standard deviation of the mean.

As the distribution is symmetric, there is a 34%
probability (68% ÷ 2) that a data point will have a value between the
mean and one standard deviation greater than the mean, and a 34%
probability that a data point will have a value between the mean and
one standard deviation less than the mean. And so on.

Virtually all of the data points (99.7%) can be expected to
be within three standard deviations of the mean.